Get a better paying job

I am facing a difficult choice now. Two companies have offered me a similar position. Company A is a big company with good reputation and a long history. Experience there will look on the resume and I can learn a lot at the job. Company B is a new subsidiary of a middle size company. The size of the company is small, and the future of the company is anyone’s guess. The problem is company B offered almost twice as much the salary as company A. Should I choose security and experience over salary?

I wasn’t able to send out resume for the past few days because of the fear of rejection. Then I realized that if you don’t do anything, it is as bad as being rejected. So I decided that I would at least try, not worrying about rejection.
I wasn’t really serious about career in the past 2 years. People with similar qualifications as mine are getting paid much better than I do. You have to know what you want, get to know the right people, and choose smart. That is why some people have a better-paying and less stressful jobs.